Step 2: Find the derivative of the function, which is f'(x). To do this, use the power rule: the derivative of x^n is n*x^(n-1).
Step 3: Apply the power rule to each term in f(x):
- For 3x^2, the derivative is 2*3x^(2-1) = 6x.
- For 2x, the derivative is 2.
Step 4: Combine the derivatives from Step 3 to get f'(x) = 6x + 2.
Step 5: Now, substitute x = 2 into the derivative f'(x). So, calculate f'(2) = 6(2) + 2.
Step 6: Perform the multiplication: 6(2) = 12.
Step 7: Add 12 and 2 together: 12 + 2 = 14.
Step 8: Therefore, f'(2) = 14.
Differentiation – The process of finding the derivative of a function, which represents the rate of change of the function with respect to its variable.
Evaluation of Derivatives – Substituting a specific value into the derivative function to find the slope of the tangent line at that point.
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